AP 10th Class Maths Important Questions Chapter 2 Sets

These AP 10th Class Maths Chapter Wise Important Questions Chapter 2 Sets will help students prepare well for the exams.

AP State Syllabus 10th Class Maths 2nd Lesson Important Questions and Answers 2 Sets

Question 1.
Write roster and builder form of “The set of all natural numbers which di-vide 42”.
Solution:
Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42
So roster form = {1, 2, 3, 6, 7, 14, 21, 42}
The builder form = {x/x ∈ N, x is a factor of 42}

Question 2.
Write A = {1, 2, 3, 4} in set builder form.
Solution:
The given set A = {1, 2, 3, 4}
The set builder form is A = {x/x ∈ N, x < 5}

AP 10th Class Maths Important Questions Chapter 2 Sets

Question 3.
Write all the subsets of B = {p, q}
Solution:
{p}, {q}, {p, q} and { } are the subsets of the given set B = {p, q}
As the n(B) = 2 then number of all sub-sets = 2n = 22 = 4

Question 4.
Write the following set {x : x = 2n + 1 and n ∈ N} in roster form.
Solution:
If n = 1 then 2n + 1 = 2(1) + 1
= 2 + 1 = 3
If n = 2 then 2n + 1 = 2(2) + 1
= 4 + 1 = 5
If n = 3 then 2n + 1 = 2(3) + 1 ‘
= 6 + 1 = 7
So {3, 5, 7, 9, } is the roster form of given set.

Question 5.
Give any two examples of disjoint sets from your daily life. ^j^Jiiae 1161
Solution:
I) A’ is set of Boys bom on Sunday
, ‘B’ is set of Boys born on Monday
Then A and B disjoint sets
∵ A ∩ B = Φ

II) P is a set of all Indians .
Q is a set of all Russians
then P ∩ Q = Φ
Hence P, Q are disjoint sets.

Question 6.
If A = {Prime numbers less than 10}, and B = {Positive odd numbers less than 10}, then find (i) A ∩ B (ii) B – A.
Solution:
A = {Prime numbers less than 10} and
B = {Positive odd numbers less than 10}
∴ A = {2, 3, 5, 7},B = {1,3,5, 7, 9}
∴ (A ∩ B) = {2, 3, 5, 7} ∩ {1,3, 5,7, 9} = {3,5,7} — (1)
and (B – A) = {1, 3, 5, 7, 9} – {2,3, 5,7} = {1,9} —–(2)

Question 7.
Write A = {3, 9,27, 81} in set – builder form.
Solution:
A = {x/x = 3n, n ∈ N and n < 5}

Question 8.
Write A = {2, 4, 8, 16} in set-builder form.
Solution:
Given set A = {2, 4, 8, 16}
Set builder form of A = {2x/x ∈ N, x < 5}

AP 10th Class Maths Important Questions Chapter 2 Sets

Question 9.
If A = \(\left\{\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \frac{1}{32}\right\}\) then write it in set-builder form.
Solution:
AP 10th Class Maths Important Questions Chapter 2 Sets 1

Question 10.
Write the set builder form of A = \(\left\{1, \frac{1}{4}, \frac{1}{9}, \frac{1}{16}, \frac{1}{25}\right\}\)
Solution:
\(\left\{1, \frac{1}{4}, \frac{1}{9}, \frac{1}{16}, \frac{1}{25}\right\}\) are in the form of \(\frac{1}{\mathrm{p}^{2}}\) whereas p < 6
So, A = {x : x = \(\frac{1}{\mathrm{p}^{2}}\); p ∈ N, and p < 6} is the set builder form.

Question 11.
Given A = {x : x is an even number less than 10}
B = {x : x is a prime number Less than 10} find A ∩ B.
Solution:
Given A = (x : x is an even number less then 10}
∴ A = {2,4, 6, 8}
and B = {x : x is a prime number less than 10}
∴ B = {2, 3, 5, 7}
A ∩ B = {2,4, 6, 8} ∩ {2, 3, 5, 7}
∴ A ∩ B = {2}

Question 12.
Set A is a sub set of set B. If n(A) = 4 and n(B) = 7, then find n(A ∪ B).
Solution:
A ⊂ B; n(A) = 4 and n(B) = 7
n(A ∪ B) = 7

Question 13.
Give one example for each question to set A and B, such that
i) A ∪ B = B, ii) A ∩ B = B.
Solution:
i) Let A = {1, 2, 3} and
B = {1,2,3,4, 5}
A ∪ B = {1,2, 3} ∪ {1, 2, 3, 4, 5}
= {1,2, 3,4, 5} = B
∴ A ∪ B = B

ii) Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10,….}
B = {2, 4,’6, 8, 10, …..}
A ∩ B = {1, 2, 3, 4, 5, 6, 7, 8,9,10,….} ∩ {2, 4, 6, 8, 10, …}
= {2, 4, 6, 8, 10, …..} = B
∴ A ∩ B = B

Question 13.
If A = {5, 6, 7}, B = {6, 7, 8, 9} find A – (A – B) and A ∩ B. What is your observation?
Solution:
A = {5, 7}, B = {6, 7, 8, 9}
A – B = {5, 6, 7} – {6, 7, 8, 9}
= {5, 6, 7, 8, 9} = {5}
A – (A – B) = {5, 6, 7} – {5} = {6, 7}
A ∩ B – {5, 6, 7} ∩ {6, 7, 8, 9} = {6, 7}
We observe that A – (A – B) = A ∩ B.

Question 14.
Read the diagram and answer the questions given below.
AP 10th Class Maths Important Questions Chapter 2 Sets 2
Find:
i) A ∪ B
ii) A – B
Solution:
i) A ∪ B = {1, 5, 6, 7, 8, 10, 11, 12}
ii) A – B = {1, 5, 6}

AP 10th Class Maths Important Questions Chapter 2 Sets

Question 15.
Let A = {x/x is an even number}
B = {x/x is an odd number}
C — {x/x is a prime number}
D = {x/x is a multiple of 5} Find
i) A ∪ B, ii) A ∩ B iii) C – D iv) A ∩ C.
Solution:
A = {x : x is an even number}
= {2,4,6,8,10 }
B = {x : x is an odd number}
= {1/3, 5,7,9, }
C = {x ; x is a prime number}
= {2,3,5,7,11, }
D = {x : x is a multiple of 5}
= {5, 10, 15, 20, 25, }
i) A ∪ B = {2, 4, 6, 8, 10, }∪{1,3, 5, 7, 9, ………..}
= {1,2,3,4,5,6,7,8,9,10……}

ii) A ∩ B = {2, 4, 6, 8, 10, …………… } ∩ {1,3, 5, 7,9, ……. }
= {} = Φ

iii) C – D = {2, 3, 5, 7, 11, ………..} – {5, 10, 15, 20, 25, …………. }
= {2,3,7, 11, ……….. }

iv) A ∩ C = {2, 4, 6, 8, 10, ………….. } ∩{2,3,5,7,11 ………….. }
= {2}

Question 16.
If A = {1,2,3, 4} and
B = {I, 2, 3, 5, 6} then find
i) A ∩ B, ii) B ∩ A iii) A – B and iv) B – C then comment on the above
Solution:
Given A = {1, 2, 3, 4} and
B = {1, 2, 3, 5, 6} then
i) A ∩ B = {1, 2, 3, 4} ∩ {1, 2, 3, 5, 6}
= {1,2,3}
ii) B ∩ A= {1,2, 3, 5, 6} ∩ {l,2, 3, 4}
= {1,2, 3}
So A ∩ B = B ∩ A
iii) A – B = {1,2, 3, 4} – {1,2, 3, 5,6}
= {4}
iv) B – A= {1,2, 3, 5, 6} – {1,2, 3, 4}
= {5,6}
So A – B ≠ B – A.

Question 17.
If A = {x : x is natural number}, B = {x: x is an even natural number}, C = {x, x is an odd natural number}, then find A ∩ B, A ∩ C, A – B, A – C and describe sets in set builder form.
Solution:
A = {1, 2, 3, 4, ………….}
B = {2,4, 6, 8, ………….. }; C = {1,3,5,7, ………….. }
For finding,
A∩B = {1,2,3,4, } ∩ {2,4,6,8, …. }
= {2, 4, 6, 8…………. }
= {x/x is an even natural number}
For finding,
A ∩ C = {1,2,3,4,…….} ∩ {1,3,5,7, ………. }
= {1,3,5,7 :…….}
A = {x/x is an odd natural number}
For findging
A – B = {1,2,3,4, ……….. } – {2,4,6,8, …………… }
= {1,3,5, ………….. }
= {x/x is an odd natural number}
For finding
A – C = {1,2,3,4,…….}-{1,3,5,7, }
= {2,4,6,8, ,…}
= {x/x is an even natural number}

AP 10th Class Maths Important Questions Chapter 2 Sets

Question 18.
If A = {3, 6, 9, 12, 15, 18,21},
B = {4, 8, 12, 16, 20}; then check whether A ∪ B = B ∪ A and A – B = B – A
Solution:
A ∪ B = {3,6,9,12,15,18,21}∪ {4,8,12,16,20}
= {3,4,6,8,9,12,15,16,18,20,21}
B ∪ A = {4,8,12,16,20} ∪ {3,6,9,12,15,18,21}
= {3,4,6,8,9,12,15,16,18,20,21}
A ∪ B = B ∪ A
A – B = {3,6,9,12,15,18,21} – {4,8,12,16,20} = {3,6,9,15,18,21}
B – A= {4,8,12,16,20} – {3,6,9,12,15,18,21} = {4,8,16,20}
A – B ≠ B – A

Question 19.
If A = {x : x is a natural number }
B = {x : x is an even number}
C = {x : x is an odd number }
D = {x : x is a prime number} then find A∪B,A∩C,B∩C and B ∩ D. Wbat do you notice ?
Solution:
A = {x : x is a natural number}
= {1,2,3, , }
B = {x : x is an even number}
= {2,4,6, }
C = {x : x is an odd number} .
= {1,3,5, …}
D = {x : x is a prime number = {2,3,5, }
A ∪ B = {1, 2, 3 …………}{2, 4, 6……………. }
= {1,2,3……………}
A ∩ C = {1, 2, 3…………. } ∩ {1, 3, 5………….. }
= {1, 3, 5………….. }
B ∩ C = {2,4,6……. }∩{1,3,5……….. }
= {} = ø
B ∩ D = {2,4,6,…} ∩ {2,3,5,…} = {2}
Noticed that A∪ B = A
A ∩ C = C

Question 20.
If A = {x : x is a natural number less than is 6}
B = {x : x is a prime number which is a divisor of 60} ,
C = {x : x is an odd natural number less than 10}
D = {x : x is an even natural number which is a divisor of 48}
Then write roster form for all above sets and find
i) A ∪ B
ii) B ∩ C
iii) A – D
iv) D – B
Solution:
Given sets in roster form.
A= {1,2, 3,4, 5}, B = {1,2, 3, 5}
C = {1, 3, 5, 7, 9}
D = {2, 4, 6, 8, 12, 16, 24}
i) A∪B = {1,2,5,4,5} ∪ {l,2,3,5}
= {1,2,3,4,5}
ii) B ∩C = {l,2,3,5} ∩ {l,3, 5,7,9}
= {1,3, 5}
iii) A – D. = {1,2, 3, 4,5} – {2, 4, 6, 8, 12, 16, 24}
= {1,3,5}
iv) D – B = {2, 4, 6, 8, 12, 16, 24} – {1,2, 3, 5}
= {4,6,8,12,16,24}

Question 21.
If A = {x : x is an even natural number and x < 12},
B = {x : x is a natural number and divisor of 6},
then find i) (A ∪ B) – (A ∩ B),
ii) (A – B) ∪ (B – A) What do you notice ?
Solution:
A = {2, 4, 6, 8, 10}; B = {1, 2, 3, 6}
A ∪ B = {2, 4, 6, 8, 10} ∪ {1, 2, 3, 6}
= {1,2,3,4,6,8,10}
A ∩ B = {2, 4, 6, 8, 10} ∩ {1, 2, 3, 6}
= {2, 6}
(A ∪ B) – (A ∩ B) = {1, 2, 3, 4, 6, 8, 10} – {2,6} = {1,3,4,8,10}
A – B = {2,4, 6, 8, 10} -{1,2, 3, 6}. ‘
= {4, 8, 10}
B – A = {1,2, 3, 6}-{2, 4, 6, 8, 10}
= {1,3}
(A – B) ∪ (B – A)- {4, 8, 10} ∪ {1,3}
= {1,3,4, 8, 10}
Noticed that (A ∪ B) – (A ∩ B) = (A – B) ∪ (B – A)

Question 22.
If A = {x/x e W, x < 10}
B = {x/x is a factor of 10}
C = {12, 22, 32,102}, then
Find i) A ∪ B ii) A ∩ B iii) A – C iv) B – C
Solution:
Given A = {x/x e W, x < 10}
B = {x/x is a factor of 10}
C = {12, 22, 32, ………….. 102},
So A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
B = {1,2, 5, 10}
C = {1,4, 9,16,25,36,49,64, 81,100}

AP 10th Class Maths Important Questions Chapter 2 Sets

i) A ∪ B
= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} ∪ {1,2,5,10}
= {0, 1,2, 3, 4, 5, 6, 7, 8, 9, 10} ……. (1)
ii) A ∩ B = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} ∩ {1,2, 5, 10} = {1,2, 5} ………….. (2)
iii) A – C = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} – {1,4,9,16,25,36,49, 64, 81, 100}
= {0, 2, 3, 5,6, 7, 8} ……………. (3)
iv) B – C = {1, 2, 5, 10}- {1,4,9,16,25,36,49,64, 81, 100}
= {2, 5, 10} ……………(4)

Question 23.
If A = {x:x is a prime number and x < 20} B = {x : x = 2x + 1, x ∈ W and x < 9), find i) A ∩ B
ii) B ∩ A
iii) A – B
iv) B – A What do you observe ?
Solution:
A = {2, 3, 5, 7, 11, 13, 17, 19}
B = {1, 3, 5, 7}
i) A ∩ B = {2, 3, 5, 7,11, 13,17,19} ∩ {1,3, 5,7}
= {3,5,7} .
ii) B ∩ A = {1, 3, 5, 7} ∩ {2, 3, 5, 7, 11, 13, 17, 19} = {3,5,7}
iii) A – B = {2, 3,5,7, 11, 13, 17, 19} – {1,3, 5,7}
= {2, 11, 13, 17, 19}
iv) B – A = {1,3,5, 7} – {2, 3, 5, 7, li; 13, 17, 19}
= {1}
∴ We observed A ∩ B = B ∩ A
A – B ≠ B – A

Question 24.
A = {- 2, 1, 3, 4, 5}, B = {7, 3, 5, 2, 8} and C = {- 2, 4, 5, 8, 9}.
Find the following sets.
i) A – (B ∪ C), ii) (A – B) ∩ (A – C).
What is your observation ?
Solution:
A = {-2, 1, 3, 4, 5}; B = {7, 3, 5, 2, 8}, C = {- 2, 4, 5, 8, 9}
i) A – (B ∪ C)
B ∪ C = {7, 3, 5, 2, 8} ∪ {- i, 4, 5, 8, 9} = {-2, 2, 3, 4, 5, 7, 8, 9}
A – (B ∪ C) = {-2, 1, 3, 4, 5}- {-2, 2, 3, 4, 5, 7, 8, 9}
= {1}

ii) (A – B) ∩ (A – C)
A – B = {-2, 1,3,4, 5} – {7, 3, 5, 2, 8} = {-2,1,4}
A – C ={-2,1,3,4,5} – { – 2,4, 5,8,9)
= {1, 3)
(A – B) ∩ (A – C)= {-2, 1,4} ∩ {1,3}
= {1}
∴ A – (B ∪ C) = (A – B) ∩ (A – C)

AP 10th Class Maths Important Questions Chapter 2 Sets

Question 25.
A = {Regular Polygons}, B = {Triangles} and C = {Quadrilaterals}. Find
i) A ∩ B ii) A ∩ C iii) A – B iv) A – C
Solution:
A = {Triangles, Quadrilaterals, Pentagon, Hexagon, Heptagon}
B = {Triangles}; C = {Quadrilaterals}
i) A ∩ B = {Triangles, Quadrilaterals, Pentagon, Hexagon, Heptagon} ∩ {Triangles} =  {Triangles}
ii) A ∩ C = {Triangles, Quadrilaterals, Pentagon, Hexagon, Heptagon} ∩ {Quadrilaterals} = {Quadrilaterals}
iii) A-B = {Triangles, Quadrilaterals, Pentagon, Hexagon, Heptagon} – {Triangles} = {Quadrilaterals, Pentagon, Hexagon, Heptagon}
iv) A – C = {Triangles, Quadrilaterals, Pentagon; Hexagon, Heptagon} – {Quadrilaterals}
= {Triangles, Pentagon, Hexagon, Heptagon}

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